A12_2011 - n =0 (-1) n x 2 n 2 2 n ( n !) 2 converges for...

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The problems and proofs on this sheet and on assignment 11 pertain to lecture material covered in the last two weeks of classes. These are provided in order to assist you with your final exam preparations. Specifically, these allow you to test your understanding and to further practise working with series and power series. Some POWER SERIES Problems: 1. Show the power series X
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Unformatted text preview: n =0 (-1) n x 2 n 2 2 n ( n !) 2 converges for all x . 2. Find the radius of convergence for the power series: (a) X n =1 3-n n x 2 n (b) X n =1 1 3 5 (2 n-1) 2 5 8 (3 n-1) x n 3. Find the interval of convergence for the power series: (a) X n =1 n b n ( x-a ) n , where a,b R and b > (b) X n =1 2 n n 2 ( x-3) n 1...
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This note was uploaded on 09/19/2011 for the course MATH 01 taught by Professor Katherine during the Summer '11 term at University of Toronto- Toronto.

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